Finite Group Databasebeta

← #14642532

Subgroups — #14642532

Order 2816.

612 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 612 conjugacy classes of subgroups — too many to draw. Only its 81 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076560C211yesmaximal, characteristic, complemented
2#13069706C211yesmaximal, characteristic, complemented
3#13069703C211yesmaximal, characteristic, complemented
4#13069689C211yesmaximal, characteristic
5#13066441C211yesmaximal, characteristic, complemented
6#13066436C211yesmaximal, characteristic, complemented
7C11×#1272C211yesmaximal, characteristic, complemented
8C22×#4325—21no—
9C22×D88—21no—
10C22×#4314—21no—
11C2×#66927C2211yescharacteristic
12C11×#391C2211yescharacteristic
13#10622844—21no—
14C2×#66885—21no—
15C2×#66885—21no—
16#10622602—21no—
17C2×#66873—21no—
18#10622552C2211yescharacteristic
19#10622542C2211yescharacteristic
20#10622286—21no—
21#10622281—21no—
22#10622278—21no—
23#10622273—21no—
24C11×#336C2211yescharacteristic
25C11×#336C2211yescharacteristic
26#10622162C2211yescharacteristic
27C22×Q8×C11D411yescharacteristic
28C22×D44—21no—
29C22×D44—21no—
30C22×D44—21no—
31C22×D44D411yescharacteristic
32C22×C4×D11—21no—
33C22×Dic22D411yescharacteristic
34C22×C8×C11—21no—
35C22×C8×C11—21no—
36C2×C11×C4⋊C4D411yescharacteristic
37C2×C42×C11C2311yescharacteristic
38C2×#4325—42no—
39C2×#4325—42no—
40C2×#4325—42no—
41C2×(C2×D11)⋊C4—21no—
42C2×(C2×D11)⋊C4—21no—
43C2×(C2×D11)⋊C4—21no—
44C2×(C2×D11)⋊C4—21no—
45C2×(C2×D11)⋊C4—21no—
46C2×C4⋊Dic11D411yescharacteristic
47C2×C4⋊Dic11D411yescharacteristic
48C2×Dic11⋊C4—21no—
49C22×C11⋊C8—21no—
50C2×D88—42no—
51C2×D88—42no—
52C2×D88—42no—
53C2×#4314—42no—
54C2×#4314—42no—
55C2×#4314—42no—
56#66927—42no—
57C11×#95—21no—
58C11×#95—21no—
59C11⋊#95—21no—
60C11⋊#95—21no—
61C11⋊#95—21no—
62C11⋊#95—21no—
63C11⋊#95—21no—
64#66885—42no—
65#66885—42no—
66#66873—42no—
67#7745—111nomaximal, Sylow
68C23×D11—21no—
69C23×D11—41no—
70C2×Q8×C11—21no—
71C2×Q8×C11—21no—
72C2×Q8×C11—41no—
73C2×Q8×C11—41no—
74C22×C4×C11—21no—
75C22×C4×C11—21no—
76C22×C4×C11C2×D411yescharacteristic
77C22×C4×C11C2×D411yescharacteristic
78C22×C4×C11C2×D411yescharacteristic
79C22×Dic11—21no—
80C22×Dic11—21no—
81C22×Dic11—21no—
82C2×D44—22no—
83C2×D44—22no—
84C2×D44—22no—
85C2×D44—21no—
86C2×D44—41no—
87C2×D44—41no—
88C2×D44—41no—
89C2×D44—41no—
90C2×D44—41no—
91C2×D44—41no—
92C2×D44—41no—
93C2×D44—41no—
94C2×D44—41no—
95C2×D44—41no—
96C2×D44—41no—
97C2×D44—41no—
98C2×D44—41no—
99C2×D44—41no—
100C2×D44—41no—
101C2×D44—41no—
102C2×D44—41no—
103C2×D44SD1612yescomplemented
104C2×C4×D11—81no—
105C2×C4×D11—81no—
106C2×C4×D11—81no—
107C2×Dic22—21no—
108C2×Dic22—21no—
109C2×Dic22—41no—
110C2×Dic22—41no—
111C2×C8×C11—22no—
112C2×C8×C11—22no—
113C2×C8×C11—41no—
114C2×C8×C11—41no—
115C2×C8×C11—41no—
116C2×C8×C11—41no—
117C11×C4⋊C4—41no—
118C42×C11—41no—
119#4325—48no—
120(C2×D11)⋊C4—41no—
121(C2×D11)⋊C4—41no—
122(C2×D11)⋊C4—41no—
123(C2×D11)⋊C4—41no—
124(C2×D11)⋊C4—81no—
125(C2×D11)⋊C4—81no—
126(C2×D11)⋊C4—81no—
127C4⋊Dic11—41no—
128C4⋊Dic11—41no—
129Dic11⋊C4—81no—
130C2×C11⋊C8—22no—
131C2×C11⋊C8—41no—
132C2×C11⋊C8—41no—
133D88—48no—
134#4314—48no—
135#2804—111no—
136#2014—111no—
137#2014—111no—
138#2011—111no—
139#1272—111no—
140#1272D1111yescharacteristic, complemented
141#1270—111no—
142C23×C11#12011yescharacteristic
143C22×D11—22no—
144C22×D11—41no—
145C22×D11—41no—
146C22×D11—41no—
147C22×D11—41no—
148C22×D11—41no—
149C22×D11—41no—
150C22×D11—42no—
151C22×D11—81no—
152C22×D11—81no—
153C22×D11—81no—
154C22×D11—81no—
155C22×D11—81no—
156C22×D11—81no—
157Q8×C11—42no—
158Q8×C11—81no—
159C2×C4×C11—21no—
160C2×C4×C11—21no—
161C2×C4×C11—21no—
162C2×C4×C11—21no—
163C2×C4×C11—21no—
164C2×C4×C11—21no—
165C2×C4×C11—41no—
166C2×C4×C11—41no—
167C2×C4×C11—41no—
168C2×C4×C11—41no—
169C2×C4×C11—41no—
170C2×C4×C11—41no—
171C2×C4×C11C2×SD1611yescharacteristic
172C2×C4×C11#13511yescharacteristic
173C2×C4×C11#13511yescharacteristic
174C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
175C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
176C2×C4×C11#13711yescharacteristic
177C2×Dic11—41no—
178C2×Dic11—41no—
179C2×Dic11—41no—
180C2×Dic11—41no—
181C2×Dic11—41no—
182C2×Dic11—41no—
183C2×Dic11—41no—
184C2×Dic11—41no—
185C2×Dic11—41no—
186D44—42no—
187D44—42no—
188D44—42no—
189D44—42no—
190D44—42no—
191D44—42no—
192D44—42no—
193D44—81no—
194D44—81no—
195D44—81no—
196D44—81no—
197D44—81no—
198D44—81no—
199D44—81no—
200C4×D11—84no—
201Dic22—42no—
202Dic22—81no—
203C8×C11—42no—
204C8×C11—42no—
205C11⋊C8—42no—
206C22×SD16—221no—
207C22×SD16—221no—
208C22×D8—221no—
209C2×#127—111no—
210C2×#102—221no—
211C2×#102—221no—
212C2×#102—221no—
213#400—221no—
214#393—221no—
215#393—221no—
216#391—111no—
217#391C2×D1111yescharacteristic
218#390—111no—
219#386—221no—
220#385—221no—
221#385—221no—
222#336—111no—
223#336C2×D1111yescharacteristic
224#336C2×D1111yescharacteristic
225C22×C11#44811yescharacteristic
226C22×C11#44911yescharacteristic
227C22×C11#44911yescharacteristic
228C22×C11#45311yescharacteristic
229C22×C11#45311yescharacteristic
230C22×C11#45311yescharacteristic
231C22×C11B(4,𝔽2)11yescharacteristic
232C2×D11—42no—
233C2×D11—42no—
234C2×D11—42no—
235C2×D11—81no—
236C2×D11—81no—
237C2×D11—81no—
238C2×D11—81no—
239C2×D11—82no—
240C2×D11—82no—
241C2×D11—82no—
242C2×D11—161no—
243C2×D11—161no—
244C2×D11—161no—
245C2×D11—161no—
246C4×C11—21no—
247C4×C11—21no—
248C4×C11—21no—
249C4×C11—21no—
250C4×C11—21no—
251C4×C11—21no—
252C4×C11—81no—
253C4×C11—81no—
254Dic11—81no—
255Dic11—81no—
256Dic11—81no—
257C22×Q8—111no—
258C22×Q8D4411yescharacteristic
259C22×D4—111no—
260C22×D4—221no—
261C22×D4—221no—
262C22×D4—221no—
263C23×C4—221no—
264C2×SD16—442no—
265C2×SD16—442no—
266C2×SD16—442no—
267C2×SD16—442no—
268C2×SD16—442no—
269C2×SD16—442no—
270C2×D8—442no—
271C2×D8—442no—
272C2×D8—442no—
273C22×C8—21no—
274C22×C8—21no—
275C22×C8—221no—
276#127—442no—
277C2×C4⋊C4—111no—
278C2×C4⋊C4—111no—
279C2×C4⋊C4—221no—
280C2×C4⋊C4D4411yescharacteristic
281C2×C22⋊C4—221no—
282C2×C22⋊C4—221no—
283C2×C22⋊C4—221no—
284C2×C22⋊C4—221no—
285C2×C22⋊C4—221no—
286C2×C42C22×D1111yescharacteristic
287#102—442no—
288#102—442no—
289#102—442no—
290#95—21no—
291#95—21no—
292#95—221no—
293#95—221no—
294#95—221no—
295#95—221no—
296#95—221no—
297C2×C11#159611yescharacteristic
298C2×C11#160011yescharacteristic
299C2×C11#160011yescharacteristic
300C2×C11#162011yescharacteristic
301C2×C11#162211yescharacteristic
302C2×C11#162211yescharacteristic
303C2×C11#165511yescharacteristic
304D11—82no—
305D11—162no—
306C24—221no—
307C24—441no—
308C2×Q8—21no—
309C2×Q8—21no—
310C2×Q8—41no—
311C2×Q8—41no—
312C2×Q8—221no—
313C2×Q8—221no—
314C2×Q8—441no—
315C2×Q8—441no—
316C2×D4—112no—
317C2×D4—222no—
318C2×D4—222no—
319C2×D4—222no—
320C2×D4—221no—
321C2×D4—441no—
322C2×D4—441no—
323C2×D4—441no—
324C2×D4—441no—
325C2×D4—441no—
326C2×D4—441no—
327C2×D4—441no—
328C2×D4—441no—
329C2×D4—441no—
330C2×D4—441no—
331C2×D4—441no—
332C2×D4—441no—
333C2×D4—441no—
334C2×D4—441no—
335C2×D4—441no—
336C2×D4—441no—
337C2×D4—441no—
338C22×C4—21no—
339C22×C4—21no—
340C22×C4—221no—
341C22×C4—221no—
342C22×C4—221no—
343C22×C4—881no—
344C22×C4—881no—
345C22×C4—881no—
346C22×C4C2×D4411yescharacteristic
347C22×C4D4×D1111yescharacteristic
348C22×C4D4×D1111yescharacteristic
349SD16—448no—
350SD16—448no—
351D8—448no—
352C2×C8—22no—
353C2×C8—22no—
354C2×C8—41no—
355C2×C8—41no—
356C2×C8—41no—
357C2×C8—41no—
358C2×C8—222no—
359C2×C8—441no—
360C2×C8—441no—
361C4⋊C4—41no—
362C4⋊C4—441no—
363C4⋊C4—441no—
364C4⋊C4—881no—
365C22⋊C4—441no—
366C22⋊C4—441no—
367C22⋊C4—441no—
368C22⋊C4—441no—
369C22⋊C4—881no—
370C22⋊C4—881no—
371C22⋊C4—881no—
372C42—41no—
373C11#774511yescharacteristic, complemented, Sylow
374C23—222no—
375C23—441no—
376C23—441no—
377C23—441no—
378C23—441no—
379C23—441no—
380C23—441no—
381C23—442no—
382C23—881no—
383C23—881no—
384C23—881no—
385C23—881no—
386C23—881no—
387C23—881no—
388C23#6693511yescharacteristic
389Q8—42no—
390Q8—81no—
391Q8—442no—
392Q8—881no—
393D4—442no—
394D4—442no—
395D4—442no—
396D4—442no—
397D4—442no—
398D4—442no—
399D4—442no—
400D4—881no—
401D4—881no—
402D4—881no—
403D4—881no—
404D4—881no—
405D4—881no—
406D4—881no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—441no—
420C2×C4—441no—
421C2×C4—441no—
422C2×C4—441no—
423C2×C4—441no—
424C2×C4—441no—
425C2×C4—441no—
426C2×C4—441no—
427C2×C4—441no—
428C2×C4—884no—
429C2×C4#6695711yescharacteristic
430C2×C4#6696111yescharacteristic
431C2×C4SD16×D1111yescharacteristic
432C2×C4#6696711yescharacteristic
433C2×C4#6697111yescharacteristic
434C2×C4#6697211yescharacteristic
435C8—42no—
436C8—42no—
437C8—442no—
438C22—442no—
439C22—442no—
440C22—442no—
441C22—881no—
442C22—881no—
443C22—881no—
444C22—881no—
445C22—882no—
446C22—882no—
447C22—882no—
448C22—1761no—
449C22—1761no—
450C22—1761no—
451C22—1761no—
452C22#1062234711yescharacteristic
453C22#1062235411yescharacteristic
454C22#1062236011yescharacteristic
455C22#1062241911yescharacteristic
456C22#1062242411yescharacteristic
457C22#1062243511yescharacteristic
458C22#1062243511yescharacteristic
459C4—21no—
460C4—21no—
461C4—21no—
462C4—21no—
463C4—21no—
464C4—21no—
465C4—81no—
466C4—81no—
467C4—881no—
468C4—881no—
469C4—881no—
470C2—882no—
471C2—1762no—
472C2#1306754011yescharacteristic
473C2#1306756411yescharacteristic
474C2#1306756511yescharacteristic
475C2#1306767711yescharacteristic
476C2#1306768911yescharacteristic
477C2#1306769111yescharacteristic
478C2#1306790611yescharacteristic
subgroupG/H
centerC23#66935
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1272C2
socleC23×C11#120
prime radical#13069689C2
hypercenter#1272D11
hypocenterC11#7745
LCSG ▷ C2×C42×C11 ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1272

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #13076560C2semidirect
2. #13069706C2semidirect
3. #13069703C2semidirect
5. #13066441C2semidirect
6. #13066436C2semidirect
7. C11×#1272C2semidirect
103. C2×D44SD16semidirect
140. #1272D11semidirect
373. C11#7745semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#130765602
#130697062
#130697032
#130696892
#130664412
#130664362
C11×#12722
#774511